\documentclass{article}
\usepackage{tikz-cd}
\usepackage{amsmath}
\begin{document}
\[
\begin{tikzcd}[row sep=1.4cm,column sep=1.6cm]
FU \arrow[r]\arrow[d] & \prod\limits_kF_k\bigl(U\cap \omega_k\bigr)
\arrow[r,yshift=2pt] \arrow[r,yshift=-2pt]\arrow[d]&
\prod\limits_{k,\ell}F_k\bigl(U\cap \omega_k\cap\omega_\ell\bigr) \arrow[d]
\\
\prod\limits_iFU_i \arrow[r]\arrow[d] &
\prod\limits_i\prod\limits_kF_k\bigl(U_i\cap \omega_k\bigr)
\arrow[r,yshift=2pt] \arrow[r,yshift=-2pt]\arrow[d]&
\prod\limits_i\prod\limits_{k,\ell}F_k\bigl(U_i\cap \omega_k\cap\omega_\ell\bigr)
\arrow[d]
\\
\prod\limits_{i,j}F(U_i\cap U_j) \arrow[r] &
\prod\limits_{i,j}\prod\limits_kF_k\bigl((U_i\cap U_j)\cap \omega_k\bigr)
\arrow[r,yshift=2pt]
\arrow[r,yshift=-2pt]&
\prod\limits_{i,j}\prod\limits_{k,\ell}F_k\bigl((U_i\cap U_j)\cap \omega_k\cap\omega_\ell
\bigr)
\end{tikzcd}
\]
\end{document}